Segmenting irregular shapes in images using deep region growing

ABSTRACT

A system for determining a region of interest in an image. The system includes a memory and an electronic processor. The electronic processor included in the system is connected to the memory and is configured to initialize internal states of nodes of a spatial lattice. Each node of the spatial lattice corresponds to a pixel of the image and is connected to at least one node representing a neighboring pixel of the image. The electronic processor is also configured to iteratively update, using a neural network, the internal states of each nodes in the spatial lattice using spatially gated propagation and identify the region of interest within the image based on the internal states of the nodes at a convergence of the spatial lattice.

FIELD

Embodiments described herein relate to segmenting images, such asbiomedical images and, in particular, segmenting images using a neuralnetwork gating data propagation both in time and space.

SUMMARY

Embodiments described herein relate a new type of neural network unitthat combines principles used in recurrent neural networks (RNNs) andconvolutional neural networks (CNNs). A RNN receives an input sequence,and reads and processes one element of the sequence at a time. As theRNN processes each element in the sequence, the RNN modifies itsknowledge about the sequence, which is stored in the RNN's internalstate. A RNN uses some or all of the internal state to either output asecond sequence or make a single prediction after it has read all of theinput sequence. An example of a RNN is a Long Short-Term Memory (LSTM)neural network that includes one or more LSTM cells. Each LSTM cellstores previous states for the cell, which can be provided to othercomponents of the LSTM neural network. Each LSTM cell includes an inputgate, a forget gate, and an output gate. The LSTM was introduced toresolve a problem with RNN training related to vanishing gradients.

A CNN applies filters (kernels) to an input (for example, an image) tomake a prediction about the input. In one example, the prediction iswhich of a set of categories the image belongs to. Filters correspond tofeatures that may be found in the input image. For example, when animage is input to a CNN, the filters are applied to blocks of adjacentpixels in the input image, to produce an intermediate image thatindicates how strongly each feature is represented at each position inthe image. The content a feature is indicated by the weights of thefilter associated with the feature. The weights multiply the pixelsincluded in each block of adjacent pixels. For example, if the input tothe CNN is a handwritten digit then the CNN classifies the handwrittendigit as a belonging to one of a plurality of categories (in this casethe categories are the numbers 1-9). The CNN's classification of thehandwritten digit is based on the features of the image that the CNNfound to be associated with the digit and how strongly those featuresindicate that the handwritten digit is one of the numbers 1-9.

Embodiments described herein relate to biomedical image segmentation.Biomedical image segmentation involves identifying boundaries of objectsin images, specifically in medical images. Region growing was previouslyused to identify objects in images. With region growing, a seed pixel isplaced somewhere within an object of interest. Once placed in the image,the seed pixel is repeatedly spread to adjacent pixels of similarintensity or brightness. Spreading of the pixel stops when a boundary ofthe object is reached. In region growing, a boundary may be defined by adrop below a threshold intensity or brightness.

One problem with region growing is that even a tiny connection to anadjacent bright pixel in a medical image can cause the region to spreadoutside the object of interest. For example, if, as shown in FIG. 1, twobright tissue regions (one tissue region located inside the lung and onetissue region located outside of the lung) are connected by a small,bright tissue fragment, region growing will incorrectly show the twobright tissue regions as belonging to the same mass or object.Accordingly, region growing is often discarded in favor of moresophisticated methods, such as level sets, conditional random fields(CRFs), active contours, and graph cuts.

CNNs discard the primacy of pixel adjacency. Rather, CNNs identifyobjects that have regularity. An object having regularity allows the CNNto be trained to classify the object as a type of object. However, CNNsmay not be able to accurately recognize and segment shapes that are notregular, such as tumor masses, lesions, and the like. Thus, CNNs oftenfail to accurately determine the boundaries of irregular shapes inmedical images, such as shapes that vary in geometry, intensity, or thelike.

Accordingly, embodiments described herein provide a technical solutionto the problems described above with response to previous solutions foridentifying the boundaries of irregularly-shaped objects of interest.Specifically, embodiments described herein incorporate the spatialconnectivity of a CNN with temporal gating as used in RNNs to provide asmarter method for segmenting irregular structures in images. Inparticular, embodiments described herein provide a new type of unit forclassifying pixels in an image based on the previous internal states andthe current values of the nodes that represent pixels adjacent to thepixel that is being classified. This new type of unit is referred toherein as a gated spatiotemporal unit, which is a gated recurrent unitwith spatial awareness normally associated with a CNN. For example, ateach time step, each node decides whether or not to update its internalstate with the value of its previous internal state or the internalstate of one of its neighboring nodes.

Accordingly, the methods and systems described herein provide a neuralnetwork that propagates information over both time and space. Ascompared to merely gating the flow of information over time, gating overboth time and space allows a recurrent unit to make decisions about aninternal state of a pixel based on the internal states and values ofsurrounding pixels in the image. Also, in some embodiments, the neuralnetwork can propagate information between image resolutions over bothtime and space.

As described in more detail below, embodiments described herein usemachine learning to learn an algorithm. In particular, the networkupdates until the values associated with internal states converge. Incontrast, a single pass network learns a function. As noted above,embodiments herein provide a gated spatiotemporal unit that controls howmuch information spreads from one pixel to another. As described in moredetail below, in some embodiments an image is input to the system, andthe system creates an image pyramid including a plurality of layers.Each layer of the image pyramid includes a different number of variablesthat represent the input image. The base of the pyramid includes a largenumber of values that represent the image (in other words, the baselayer represents the image at a high resolution). At each successivelevel of the pyramid fewer and fewer values are used to represent theimage (in other words, each successive layer represents the image at alower resolution than the most previous layer). The image pyramid allowsinformation from one part of the image to propagate to a lowerresolution and then back to a higher resolution in a different part ofthe image, in fewer iterations than if the system did not utilize animage pyramid. This is beneficial if, for example, an image withthousands of pixels is input to the system. Such an input could requirethe system to perform thousands of iterations before generating aprediction. The system performs convolutions using an internal state ofthe system from a previous time step and the representations of theimage in the image pyramid. The results of the convolutional layers areused by the gated spatiotemporal unit to determine values to include ina current internal state of a node in the network. Iterations areperformed over the gated spatiotemporal unit until the internal statesof the nodes in the network converge. When the internal states of thenodes in the system converge, a probability that each pixel belongs toan object of interest is calculated. In particular, embodimentsdescribed herein provide a network for segmenting non-regular structuresin medical images that is intelligent about how the data flows over thelattice and learns other factors, such as homogeneity, to determine howto spread the pixel. However, these embodiments may be applicable indomains other than medical imaging segmentation, including, for example,weather prediction, oil and gas modeling, and the like.

For example, one embodiment provides a method for identifying an objectof interest in a medical image. The method includes initializinginternal states of nodes of a spatial lattice. Each node in the spatiallattice corresponds to a pixel of the medical image and is connected toat least one node representing a neighboring pixel of the medical image.The method also includes iteratively updating, using a neural network,the internal states of the nodes in the spatial lattice using spatiallygated propagation. At each iteration, each node updates its internalstate based on at least one selected from the group consisting of avalue of the node from a previous iteration, a value of a neighboringnode from the previous iteration, and a new value of the node. Themethod further includes identifying the object of interest within themedical image based on the values of the nodes at a convergence of thespatial lattice.

Another embodiment also provides a method for identifying an object ofinterest in a medical image. However, the method provided by thisembodiment includes creating an image pyramid for the medical image. Thecreated image pyramid includes a plurality of layers, each layerincludes a plurality of values, and each value represents a block of oneor more pixels in the medical image. Each successive layer in the imagepyramid includes fewer values than the most previous layer. The methodalso includes, for each layer of the image pyramid, initializinginternal states of nodes of a spatial lattice. Each node in the spatiallattice represents a block of one or more pixels in the medical imageand is connected to at least one node representing a neighboring blockof one or more pixels in the medical image. The method also includes,for each layer of the image pyramid, iteratively updating, using aneural network, the internal states of the nodes in the spatial latticeusing spatially gated propagation. At each iteration, each node updatesits internal state based on at least one selected from the groupconsisting of a value of the node from a previous iteration, a value ofa neighboring node from the previous iteration, and a new value of thenode. The method further includes identifying the object of interestwithin the medical image based on the values of the nodes at aconvergence of the spatial lattice having nodes representing the valuesincluded in a first layer of the image pyramid.

One embodiment provides a system for determining a region of interest inan image. The system includes a memory and an electronic processor. Theelectronic processor included in the system is connected to the memoryand is configured to initialize internal states of nodes of a spatiallattice. Each node of the spatial lattice corresponds to a pixel of theimage and is connected to at least one node representing a neighboringpixel of the image. The electronic processor is also configured toiteratively update, using a neural network, the internal states of eachnodes in the spatial lattice using spatially gated propagation andidentify the region of interest within the image based on the internalstates of the nodes at a convergence of the spatial lattice.

Another embodiment also provides a system for determining a region ofinterest in an image. Like the system of the embodiment described above,the system described in this embodiment also includes a memory and anelectronic processor that is connected to the memory. However, theelectronic processor of the system provided by this embodiment isconfigured to create an image pyramid for the image. The image pyramidincludes a plurality of layers. For each layer of the image pyramid, theelectronic processor is configured to initialize internal states ofnodes of a spatial lattice and iteratively update, using a neuralnetwork, the internal states of the nodes in the spatial lattice usingspatially gated propagation. Each node in the spatial lattice representsa block of one or more pixels in the image and is connected to at leastone node representing a neighboring block of one or more pixels in theimage. The electronic processor is also configured to identify theregion of interest within the image based on the internal states of thenodes at a convergence of the spatial lattice having nodes representingvalues included in a first layer of the image pyramid.

One embodiment provides a non-transitory computer-readable mediumincluding instructions executable by an electronic processor to performa set of functions. The set of functions includes initializing internalstates of nodes of a spatial lattice. Each node represents a pixel of animage and is connected to at least one neighboring pixel of the image.The set of functions also includes iteratively updating, using a neuralnetwork, the internal states of the nodes in the spatial lattice usingspatially gated propagation. At each iteration, each node updates itsinternal state based on at least one selected from the group consistingof a value of the node from a previous iteration, a value of aneighboring node from the previous iteration, or a new value of thenode. The set of functions further includes identifying an object ofinterest within the image based on the values of the nodes at aconvergence of the spatial lattice.

Another embodiment also provides a non-transitory computer-readablemedium including instructions executable by an electronic processor toperform a set of functions. However, unlike the set of functions in theembodiment described above, the set of functions performed by theelectronic processor of this embodiment include creating an imagepyramid for an image. The created image pyramid includes a plurality oflayers, each layer includes a plurality of values, and each valuerepresents a block of one or more pixels in the image. Each successivelayer in the image pyramid includes fewer values than a most previouslayer. The set of functions also includes, for each layer of the imagepyramid, initializing internal states of nodes of a spatial lattice.Each node of the image pyramid represents a block of one or more pixelsin the image and is connected to at least one node representing aneighboring block of one or more pixels in of the image. The set offunctions also includes, for each layer of the image pyramid,iteratively updating, using a neural network, the internal states of thenodes in the spatial lattice using spatially gated propagation. At eachiteration, each node updates its internal state based on at least oneselected from the group consisting of a value of the node from aprevious iteration, a value of a neighboring node from the previousiteration, or a new value of the node. The set of functions furtherincludes identifying an object of interest within the image based on thevalues of the nodes at a convergence of the spatial lattice having nodesrepresenting the values included in a first layer of the image pyramid.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a medical image to which region growing has beenapplied to identify an object of interest.

FIG. 2 illustrates a system for determining a region of interest in animage.

FIG. 3 illustrates a neural network included in the system of FIG. 2.

FIG. 4 illustrates an example of input to a node in a gatedspatiotemporal unit.

FIG. 5 illustrates an example of a medical image that the neural networkof FIG. 4 receives as input.

FIG. 6 illustrates an example of a region of interest that the neuralnetwork of FIG. 4 detects in the medical image of FIG. 5.

DETAILED DESCRIPTION

One or more embodiments are described and illustrated in the followingdescription and accompanying drawings. These embodiments are not limitedto the specific details provided herein and may be modified in variousways. Furthermore, other embodiments may exist that are not describedherein. Also, the functionality described herein as being performed byone component may be performed by multiple components in a distributedmanner. Likewise, functionality performed by multiple components may beconsolidated and performed by a single component. Similarly, a componentdescribed as performing particular functionality may also performadditional functionality not described herein. For example, a device orstructure that is “configured” in a certain way is configured in atleast that way, but may also be configured in ways that are not listed.Furthermore, some embodiments described herein may include one or moreelectronic processors configured to perform the described functionalityby executing instructions stored in non-transitory, computer-readablemedium. Similarly, embodiments described herein may be implemented asnon-transitory, computer-readable medium storing instructions executableby one or more electronic processors to perform the describedfunctionality. As used in the present application, “non-transitorycomputer-readable medium” comprises all computer-readable media but doesnot consist of a transitory, propagating signal. Accordingly,non-transitory computer-readable medium may include, for example, a harddisk, a CD-ROM, an optical storage device, a magnetic storage device, aROM (Read Only Memory), a RAM (Random Access Memory), register memory, aprocessor cache, or any combination thereof.

In addition, the phraseology and terminology used herein is for thepurpose of description and should not be regarded as limiting. Forexample, the use of “including,” “containing,” “comprising,” “having,”and variations thereof herein is meant to encompass the items listedthereafter and equivalents thereof as well as additional items. Theterms “connected” and “coupled” are used broadly and encompass bothdirect and indirect connecting and coupling. Further, “connected” and“coupled” are not restricted to physical or mechanical connections orcouplings and can include electrical connections or couplings, whetherdirect or indirect. In addition, electronic communications andnotifications may be performed using wired connections, wirelessconnections, or a combination thereof and may be transmitted directly orthrough one or more intermediary devices over various types of networks,communication channels, and connections. Moreover, relational terms suchas first and second, top and bottom, and the like may be used hereinsolely to distinguish one entity or action from another entity or actionwithout necessarily requiring or implying any actual such relationshipor order between such entities or actions.

As described above, biomedical image segmentation seeks to identifypixels within an image that represent an object of interest, whichallows various calculations and data processing to be performed for theobject (for example, volume calculation and the like). Many techniquesfor performing image segmentation, however, rely on identifyingconsistent shapes and context. For example, as described above, CNNsexcel at recognizing shapes and objects in images that the CNNs havebeen trained to recognize but CNNs struggle to recognize irregularshapes in images. Accordingly, techniques relying on identifyingconsistent shapes and context may be ineffective in identifyingirregular objects, such as tumor masses, lesions, and the like.

Other techniques rely on pixel spreading to determine the boundaries ofan object of interest in an image. As described above, region growingdoes not rely on regularity but spreads a seed pixel to adjacent pixelsuntil boundaries are identified. Accordingly, the shape of an object ofinterest does not impact the performance of region growing. However, asshown in FIG. 1, when an object does not have a well-defined boundary(such as when the object is connected to adjacent bright tissue by evena small connection), region growing may improperly grow an objectoutside of its true boundary.

To solve the deficiencies of the above described techniques, embodimentsdescribed herein combine the advantages of CNNs and RNNs in aspatiotemporal unit to improve the identification of the irregularobjects in images. In particular, as described in more detail below,embodiments described herein employ spatially gated propagation. Gatinginvolves one piece of a network generating a new state for the system(based on its prior state and newly received information) and a separatepiece of the network gating this new state and deciding whether or notthe new state will be used and propagated forward in time. As describedherein, the most previous internal states of a pixel and the pixel'snearest neighbors are gated and used to determine the internal state ofthe pixel at a current time step. Therefore, the systems and methodsdescribed herein propagate values over both space and time.Additionally, the creation of the above described image pyramid allowsthe propagation of values over different image resolutions.

FIG. 2 illustrates a system 200 for implementing a neural network.Neural networks are machine learning models that employ one or morelayers of nonlinear units to predict an output for a received input.Some neural networks include one or more hidden layers in addition to aninput layer and an output layer. The output of each hidden layer is usedas input to the next layer in the network (the next hidden layer or theoutput layer). Each layer of the network generates an output from areceived input in accordance with current values of a respective set ofparameters.

As illustrated in FIG. 2, the system 200 includes a computing device202, which includes an electronic processor 204 and a memory 206. Theelectronic processor 204 and the memory 206 communicate wirelessly, overwired communication channels or buses, or a combination thereof. Thecomputing device 202 may include additional components than thoseillustrated in FIG. 2 in various configurations. For example, in someembodiments, the computing device 202 includes multiple electronicprocessors, multiple memory modules, or a combination thereof. Also, insome embodiments, the computing device 202 includes one or moreinput-output interfaces that allow the computing device 202 tocommunicate with networks, peripheral devices, and the like.

It should be understood that the functionality described herein as beingperformed by the computing device 202 may be performed in a distributednature by a plurality of computing devices located in various geographiclocations. For example, the functionality described herein as beingperformed by the computing device 202 may be performed by a plurality ofcomputing device 202 included in a cloud computing environment. Theelectronic processor 204 may be a microprocessor, anapplication-specific integrated circuit (ASIC), and the like. Theelectronic processor 204 is generally configured to execute softwareinstructions to perform a set of functions, including the functionsdescribed herein. The memory 206 includes a non-transitorycomputer-readable medium and stores data, including instructions thatare executable by the electronic processor 204. For example, asillustrated in FIG. 2, the memory 206 stores a neural network 208, whichincludes a computer program executed by the electronic processor 204.

FIG. 3 illustrates a visual representation of an example of the neuralnetwork 208 that the electronic processor 204 executes to perform themethods described herein. As illustrated in FIG. 3, when executed by theelectronic processor 204, the neural network 208 provides a machinelearning system that receives an input and generates an output 305. Asone example, the input includes an image (an input image 300), such as abiomedical image, or another type of multi-dimensional data, and theoutput 305 similarly includes an image or another type ofmulti-dimensional data.

As shown in FIG. 3, the input image 300 is input to a first layer 310 ofthe neural network 208. It should be understood that while the firstlayer 310 is illustrated as a single layer this is purely forillustrative purposes and the first layer 310 may include any number oflayers. In the first layer 310, the neural network 208 may perform aplurality of convolutions on values representing the brightness of eachpixel. In other embodiments, the neural network 208 may perform aplurality of convolutions in the first layer 310 to create an imagepyramid 315 from the input image 300 (I₀), as described below.

The image pyramid 315 is a sequence of tensors (I₁−I_(l)) convolved fromthe input image 300. The tensor produced for l=1 has the same spatialdimensions as the input image 300 (I₀), but the tensors halve in sizefor each subsequent convolution/reduction. Therefore, tensors for eachvalue of l have a different resolution, the tensor I₁ has the highestresolution, and the tensor I_(l) has the lowest resolution. Thefollowing equations illustrate the process of creating the image pyramid315, performed in the first layer 310.

I ₁ =K ₁ ^(I) *I ₀  (1)

I ₂ =K ₂ ^(I) *D ₁ ^(I) *I ₁  (2)

. . .

I _(l) =K _(l) ^(I) *D _(l−1) ^(I) *I _(l−1)  (3)

The operator * represents a convolution operation. For example, theequation A*B represents a convolution between an input B and a kernel A.

I₀ is a variable that represents the original input image 300. I₀ hasdimensions N₀×N₀×1. In other words, the input image 300 has N₀ rows, N₀columns, and (because, in this example embodiment, the input image 300is a greyscale image) one channel.

I_(l) is a variable that represents an intermediate form of image data(a tensor) produced after one or more reductions are performed on theinput image 300 (I₀). As described above, when l>1, I_(l) has a lowerresolution than the input image 300 (I₀). I_(l) has the dimensionsN_(l)×N_(l)×C, where N_(l)=2^(−(l−1))N₀ and C is the number of channels.

K_(l) ^(I) is a variable that represents a convolution operator (akernel) that preserves the dimensions of the input image data. The inputimage data has the dimensions N_(l)×N_(l)×C_(I) while the output imagedata has the dimensions N_(l)×N_(l)×C₀. K may represent the combinationof several sequential convolution operations that are arranged as in,for example, AlexNet, DenseNet, or a range of other architectures andthe learnable parameters of the convolutional operators.

D₁ ^(I) is a variable that represents a convolution operator thatreduces the dimensions of the input image data by one half. The inputimage data has the dimensions N_(l−1)×N_(l−1)×C_(I), while the outputimage data has the dimensions N_(l)×N_(l)×C₀. Like K, D may representseveral sequential convolution operations arranged as in, for example,AlexNet, DenseNet, or a range of other architectures and the learnableparameters of the convolutional operators. However, the convolutionaloperator D also represents a max-pooling or strided convolution layerthat reduces the dimensions of the input image data by half.

The tensor calculated for each level of the image pyramid 315 is fedinto a second layer 320. The equation that illustrates the operationsperformed in the second layer 320 is

X _(l) ^(t) =K _(l) ^(IH)*[I _(l) ,H _(l) ^(t)]  (4)

Again, the operator * represents a convolution operation, and I_(l) is avariable that represents an intermediate form of image data (a tensor)produced after one or more reductions are performed on the input image300 (I₀).

[A, B] is a concatenation operation between tensors, for example, thetensors A and B. A concatenation operation performed on two tensorscombines the channels included in each of the tensors. For example, ifthe tensor A has dimensions M×M×C₁ and the tensor B has dimensionsM×M×C₂, then the output of [A, B] has dimensions M×M×(C₁+C₂).

H_(l) ^(t) is a tensor 322 that holds an internal state for each node inthe spatial lattice at resolution l and time step t. As described above,the internal state of each node in the spatial lattice is updated oneach time step. The tensor 322 has the dimensions N_(l)×N_(l)×C_(H).Therefore, there are C_(H) variables describing each block of one ormore pixels of the image at resolution l.

K_(l) ^(IH) is a variable that represents a convolution operator thatpreserves the dimensions of the input image data. The input image datahas the dimensions N_(l)×N_(l)×C_(I), while the output image data hasthe dimensions N_(l)×N_(l)×C₀. K may represent the combination ofseveral sequential convolution operations that are arranged as in, forexample, AlexNet, DenseNet, or a range of other architectures and thelearnable parameters of the convolutional operators.

X_(l) ^(t) is a variable that represents the results 323 of performingthe equation (4). X_(l) ^(t) has dimensions N_(l)×N_(l)×C_(X) and isinput to the third layer 325 of the neural network 208.

In summary, equation (4) concatenates the tensor (I^(l)) with the tensor322 (H_(l) ^(t)) (performs a first concatenation), applies a convolutionoperator K_(l) ^(IH) to the concatenation (performs a first convolutionfor a current layer of the image pyramid), and saves the results 323 intensor X_(l) ^(t).

The equation that illustrates the operations performed in the thirdlayer 325 is

Z _(l) ^(t) =K ₁ ^(L3)*[D _(l) ^(X) *X _(l−1) ^(t) ,X _(l) ^(t) ,U _(l)^(X) *X _(l+1) ^(t)]  (5)

Again, as described above, the operator * represents a convolutionoperation, and [A, B] is a concatenation operation between tensors, forexample, the tensors A and B. Similarly, K_(l) ^(L3) is a variable thatrepresents a convolution operator (a kernel) that preserves thedimensions of the input image data, D_(l) ^(X) is a variable thatrepresents a convolution operator (a kernel) that reduces the dimensionsof the input image data by one half, and X_(l) ^(t) is a variablerepresenting the result of the equation (4) calculated from the tensorI_(l), the internal state H_(l) ^(t), and the kernel K_(l) ^(IH).

X_(l+1) ^(t) is a variable representing the result of the equation (5)calculated from the tensor I_(l+1), the internal state H_(l+1) ^(t), andthe kernel K_(l+1) ^(IH), and X_(l−1) ^(t) is a variable representingthe result of the equation (5) calculated from the tensor I_(l−1), theinternal state H_(l−1) ^(t), and the kernel K_(l−1) ^(IH).

U_(l) ^(X) is a variable that represents a convolution operator (akernel) that upsamples the dimensions of the input image data bydoubling the dimensions. For example if the input image data has thedimensions N_(l+1)×N_(l+1)×C_(I), the output image data has thedimensions N_(l)×N_(l)×C₀. Like the convolutional operator K, theconvolutional operator U may represent the combination of severalsequential convolution operations arranged as in AlexNet, DenseNet, or arange of other architectures and the learnable parameters of theconvolutional operations. However, the convolutional operator U may alsorepresent a transposed convolution layer to double the image dimensions.

Z_(l) ^(t) is a tensor that includes the result of performing equation(5). Z_(l) ^(t) contains information to be passed to a gatedspatiotemporal unit. In summary, equation (5) includes reducing theresults (X_(l−1) ^(t)) of calculating equation (4) with a tensorrepresenting the input image 300 at a higher resolution (I_(l−1)) (alayer of the image pyramid directly below the current layer of the imagepyramid) and upsampling the results (X_(l+1) ^(t)) of calculatingequation (4) from a tensor representing the input image 300 at a lowerresolution (I_(l+1)) (a layer of the image pyramid directly above thecurrent layer of the image pyramid). Equation (5) also includesconcatenating the results of the upsampling with the results of thedownsampling, and with the results of calculating equation (4) from atensor representing the input image 300 at a resolution I_(l) (performsa second concatenation). The equation convolves the results of theconcatenation with the kernel K_(l) ^(L3) (performs a secondconvolution) and saves the results in the variable Z_(l) ^(t).

In the first iteration of the neural network 208 merely initializes theinternal state for each node included in a spatial lattice of a gatedspatiotemporal unit 330 using the output from the third layer 325. Eachnode includes a vector of values that represent the internal state ofthe node, and values derived in the image pyramid from the brightness ofa block of one or more pixels centered at that node. In each successiveiteration, the internal state of each node from the previous iterationis input into the second layer 320 of the neural network 208, via thetensor 322 (H_(l) ^(t)). The process described above is then repeatedstarting at the second layer 320.

As described above, the neural network 208 includes the gatedspatiotemporal unit 330 with a plurality of nodes arranged in a spatiallattice. Each node in this lattice corresponds to a pixel in the inputimage 300. The gated spatiotemporal unit 330 performs data processing ateach of multiple time steps. At each time step, the gated spatiotemporalunit 330 receives a plurality of values. Based on the received valuesand the values representing the internal state of each node that weregated in the previous time step, the gated spatiotemporal unit 330determines how to update internal state of each node at the current timestep. As will be described in more detail below, the gatedspatiotemporal unit 330 determines how to update the internal state ofeach node by deciding, for each node in the lattice, whether to maintainthe internal state of the node at a previous time step, set the node'sinternal state to a value representing the internal state neighboringnode from a previous time step, or generate a new internal state for thenode.

The following equation is an example of a computation used to determinethe internal state H_(l) ^(t+1) 327 of a node included in the lattice ofthe gated spatiotemporal unit 330 at the current time step and isdistributed over seven lines (labeled I-VII) for ease of interpretation.

H _(l) ^(t+1)=tan h[  (I)

σ(Z _(l,1) ^(t))⊙S _(0,0) *H _(l) ^(t)  (II)

+σ(Z _(l,2) ^(t))⊙S _(0,−1) *H _(l) ^(t)  (III)

+σ(Z _(l,3) ^(t))⊙S _(−1,0) *H _(l) ^(t)  (IV)

+σ(Z _(l,4) ^(t))⊙S _(1,0) *H _(l) ^(t)  (V)

+σ(Z _(l,5) ^(t))⊙S _(0,1) *H _(l) ^(t)  (VI)

+σ(Z _(l,6) ^(t))⊙ tan h(Z _(l,7) ^(t))]  (6)(VII)

σ(A) represents the application of the sigmoid function 1/(1+e^(−a))element wise to every element a of the tensor A. The sigmoid functionmay be referred to as a “squashing” function. The sigmoid function takesin an input value anywhere from +∞ to −∞ and squashes the input value toan output value from 0 to 1.

Tan h is also a squashing function. It also takes in an input valueanywhere from +∞ to −∞ but the tan h function squashes the input valueto an output value from −1 to 1.

The operator ⊙ represents a Hadamard product operation. If, given theequation A⊙B for example, a Hadamard product operation between input Band input A is performed. The Hadamard product is an element wisemultiplication of each pair of elements from two identically sizedinputs.

Z_(l) ^(t) is a tensor that contains the results 326 of the computationperformed at the third layer 325 at resolution l and time step t. Z_(l)^(t) has dimensions N_(l)×N_(l)×7×C_(H). Each of the seven elements ofthe third dimension has a specific role in the spatiotemporal gatingprocess. The variables Z_(l,1) ^(t) through Z_(l,7) ^(t) in the equationrefer to the tensor that results when one of the seven elements isselected. Each tensor associated with each of the seven elements has thedimensions N_(l)×N_(l)×C_(H).

H_(l) ^(t) is a tensor 322 that holds an internal state for each node inthe spatial lattice at resolution l and time step t. As described above,the internal state is dynamically updated at each time step. The tensorhas the dimensions N_(l)×N_(l)×C_(H). Therefore, there are C_(H)variables describing each node at resolution l.

S_(Δx,Δy) is a spatial shifting convolution operator. It has nolearnable parameters. S_(Δx,Δy) allows information from the internalstates of nearest neighbor nodes to be considered when determining thecurrent internal state of a node.

Returning to the equation above, the results 326 that are stored in thetensor Z_(l) ^(t) are broken into seven parts. Each part represents anelement in the third dimension of the tensor Z_(l) ^(t), as describedabove. Line (I) of equation (6) applies a tan h squashing function tothe sum of lines II-VII of equation (6) to determine the internal stateof a node at the current iteration. Line (II) of equation (6)corresponds to the possibility of copying the internal state of the nodefrom the previous time stamp to the current time stamp, depending on thegated value. The next four lines (III-VI) (+σ(Z_(l,2)^(t))⊙S_(0,−1)*H_(l) ^(t), +σ(Z_(l,3) ^(t))⊙S_(−1,0)*H_(l) ^(t),+σ(Z_(l,4) ^(t))⊙S_(1,0)*H_(l) ^(t), +σ(Z_(l,5) ^(t))⊙S_(0,1)*H_(l)^(t)) each correspond to the possibility of copying the internal statesof one of the nearest neighbors from the previous iteration to theinternal state of the node in the current iteration. The last line (VII)corresponds to generating a completely new value and possibly settingthe internal state of the node at the current iteration to the newvalue.

FIG. 4 illustrates the connections between a node 400 whose internalstate is being determined in a current iteration and nodes with internalstates that were determined at a previous iteration. Each node isconnected to nodes whose internal states were calculated at a mostprevious iteration of the gated spatiotemporal unit 330. Specifically,each node is connected to a node that represents its own internal statein the most previous iteration of the gated spatiotemporal unit 330 aswell as nodes that represent internal states of its neighboring nodes inthe most previous iteration of the gated spatiotemporal unit 330. InFIG. 4, nodes in the group 405 are nodes that are each associated withinternal states that are determined in a most previous iteration of theneural network 208. Nodes in the group 410 are nodes that are associatedwith internal states that are determined in the current iteration of theneural network 208. As described above, each node corresponds to a pixel(or block of one or more pixels) in the input image 300. Eachneighboring node of a node represents a pixel (or block of one or morepixels) that is adjacent to the pixel (or block of one or more pixels)represented by the node. For example, if a node 400 represents a pixelin the image at coordinates (i,j), then the node 400 representing thepixel at (i,j) is connected to a node 415 representing a pixel atcoordinates (i−1,j) (directly to the left of the pixel at (i,j)), a node420 representing a pixel at coordinates (i+1,j) (directly to the rightof the pixel at (i,j)), a node 425 representing a pixel at coordinates(i,j+1) (directly above the pixel at (i,j)), and a node 430 representinga pixel at coordinates (i,j−1) (directly below the pixel at (i,j)). Eachof the above nodes, described as being connected to the node 400representing the pixel (i,j), are the neighboring nodes of the node 400.Therefore, the gated spatiotemporal unit 330 determines whether to setthe internal state of the node 400 to the internal state of one of thenodes in the group 405.

When the internal states of the nodes in the spatial lattice of thegated spatiotemporal unit 330 converge (change less than a predeterminedamount), the internal states of the nodes representing the input image300 at the highest resolution are output to a final layer 335 of theneural network 208. The final layer 335 uses one value included in theinternal state of each node to calculate the probability (for example, avalue between zero and one) that the pixel that that node representsbelongs to the object of interest in the input image 300. The followingequation describes the operation performed in the final layer 335 todetermine the probability that each pixel is a part of an object ofinterest:

Y ^(t)=σ(K ₁ ^(Y) *H ₁ ^(t))  (7)

Y^(t) is a variable representing the output 305 of the neural network208 at time step t and has dimensions N₀×N₀×1 (the same dimensions asthe input).

H₁ ^(t) is a tensor that holds an internal state for each node in thespatial lattice at resolution 1 and time step t.

K₁ ^(Y) is a variable that represents a convolution operator thatpreserves the dimensions of the input image data. The input image datahas the dimensions N₀×N₀×C_(I), while the output image data has thedimensions N₀×N₀×1. K may represent the combination of severalsequential convolution operations that are arranged as in, for example,AlexNet, DenseNet, or a range of other architectures and the learnableparameters of the convolutional operators.

In summary equation (7) applies a final convolution using K₁ ^(Y) to thehighest resolution internal state H₁ ^(t), thereby reducing the numberof input channels (C_(H)) to 1 output channel. The equation applies thesigmoid function to the results of applying a final convolution using K₁^(Y) to the highest resolution internal state H₁ ^(t), thereby squashingeach value included in Y^(t) to a value between 0 and 1. Each value inY^(t) between 0 and 1 corresponds to the probability that an image pixellies inside an object of interest in the input image 300. For example,if the value produced by the sigmoid function for a single pixel is 0.5then there is a fifty percent (50%) probability that the pixel is withinthe object of interest.

The neural network 208 may store generated output 305 (the calculatedprobabilities for each node) in an output data repository (e.g., thememory 206) or provide generated output 305 for use or consumption, suchas by displaying the output 305 to a user on a display device.Regardless, the electronic processor 204 compares the probability foreach pixel that the pixel is included in an object of interest to apredetermined threshold. If the probability that a pixel is a part of anobject of interest is above a predetermined threshold, the electronicprocessor 204 determines that the pixel is a part of the object ofinterest.

It should be understood that, in some embodiments, in the neural network208 described above equations (4-6) is performed for each level ofrepresentation of the input image 300 (I₁−I_(l)) included in the imagepyramid 315. It should also be understood that while the neural network208 is described above as propagating values over time, space, andresolutions, the neural network 208 may be modified to only propagatevalues over time and space.

It should also be understood that the values of the gates used todetermine the internal state of each node at each iteration need not beeither zero or one, but may be any value between 0 or 1 (see equation(6) above). Accordingly, in some embodiments, the updated internal stateof a node may be a mixture (or, more mathematically, a linearcombination) of two or more of the options described above (a value ofthe node from a previous iteration, values of one or more neighboringnodes from a previous iteration, and a new value of the node).

FIG. 5 and FIG. 6 provide an example of a practical application of theneural network 208. FIG. 5 illustrates an example of a medical image 500that the neural network 208 may receive as input. The object of interestin the image 500 is a tumor 505 in a left lung 510. FIG. 6 illustratesthe area of the medical image 500 that the neural network 208 identifiesas an object of interest (the tumor 505). Unlike when the region growingtechnique is used (see FIG. 1), the boundaries of the object of interestdo not extend outside of the left lung 510.

Thus, embodiments described herein provide a neutral network thatincludes a spatiotemporal unit. The spatiotemporal unit is a spatiallyextended lattice of nodes. Each node corresponds, for example, to apixel in an image. The neural network determines an initial internalstate for each node and iteratively updates the internal state for eachnode to produce a new internal state over and over again by propagatingvalues over time, over space, or both and by calculating new values torepresent the internal state for each node. Accordingly, as compared toother types of RNNs, such as long short term memory (LSTM) networks andgated recurrent unit (GRU) networks that iterate on one-dimensionalsequences of letters or words, embodiments described herein consider thedecisions of neighboring nodes when updating the internal state of eachnode. In particular, embodiments described herein apply both spatial andtemporal dimensions. Accordingly, although the time dimension onlyiterates forwards, spatial gating allows spatial information to resonateback and forth over the spatial lattice for as long as needed, as newconclusions are reached in one part of the image and propagated to otherparts of the image to inform decision making at those parts.Additionally, in some embodiments described herein, values in the neuralnetwork 208 may be propagated between different resolutions of theimage.

The embodiments described herein are closed. In particular, the neuralnetwork 208 described herein is given all of the information about theoutside world as initial input (the image needing processing) and fromthat point onward the neural network 208 evolves in time only accordingto its own internal state and rules, not taking in any furtherinformation from the outside. As such, the iteration continues untilconvergence, when there are no further changes to the internal state.This makes the neural network 208 like an algorithm rather than afunction. In contrast, RNNs are given a new piece of the problem (e.g.,one word) at each time step, so the iteration continues only as long asthere is new information available.

Various features and advantages of some embodiments are set forth in thefollowing claims.

What is claimed is:
 1. A method for identifying an object of interest ina medical image, the method comprising: initializing internal states ofnodes of a spatial lattice, wherein each node corresponds to a pixel ofthe medical image and is connected to at least one node representing aneighboring pixel of the medical image; iteratively updating, using aneural network, the internal states of the nodes in the spatial latticeusing spatially gated propagation, wherein at each iteration each nodeupdates its internal state based on at least one selected from the groupconsisting of a value of the node from a previous iteration, a value ofa neighboring node from the previous iteration, and a new value of thenode; and identifying the object of interest within the medical imagebased on the values of the nodes at a convergence of the spatiallattice.
 2. The method according to claim 1, wherein iterativelyupdating, using a neural network, the internal states of the nodesincludes updating a value in a vector of values associated with theinternal states of the nodes.
 3. The method according to claim 2,wherein the values in the vector of values include a value representingthe brightness of the pixel corresponding to the node and a valuerepresenting the internal state of the node.
 4. The method according toclaim 1, wherein a convolution involving previous internal states of thenodes is performed for each iteration.
 5. The method according to claim1, wherein the method further includes performing, in a first iteration,convolutions on each value representing a brightness of each pixel. 6.The method according to claim 1, wherein identifying an object ofinterest within the medical image based on the values of the nodes at aconvergence of the spatial lattice includes using a final layer of theneural network to calculate a probability that each pixel is included inthe object of interest based on a value included in a vector of valuesassociated with each pixel; and determining, for each pixel, if thecalculated probability is above a predetermined threshold.
 7. The methodaccording to claim 1, wherein each node updates its internal state basedon at least one selected from the group consisting of a value of thenode from a previous iteration, a value of a neighboring node from theprevious iteration, and a new value of the node using a squashingfunction.
 8. The method according to claim 1, wherein the neighboringnode is one selected from a group consisting of a node that represents apixel that is directly above, directly below, to the right of, and tothe left of a pixel represented by the node.
 9. The method according toclaim 1, the method further comprising generating an image pyramid witha plurality of layers, wherein each successive layer represents themedical image with fewer values.
 10. The method according to claim 9,the method further comprising concatenating values from a plurality oflayers of the image pyramid in each iteration.
 11. A system fordetermining a region of interest in an image, the system comprising amemory; and an electronic processor, connected to the memory andconfigured to initialize internal states of nodes of a spatial lattice,wherein each node corresponds to a pixel of the image and is connectedto at least one node representing a neighboring pixel of the image,iteratively update, using a neural network, the internal states of eachnodes in the spatial lattice using spatially gated propagation; andidentify the region of interest within the image based on the internalstates of the nodes at a convergence of the spatial lattice.
 12. Thesystem according to claim 11, wherein the electronic processor isconfigured to update the internal states of the nodes by, at eachiteration, updating the internal state based on at least one selectedfrom the group consisting of a value of the node from a previousiteration, a value of a neighboring node from the previous iteration, ora new value of the node.
 13. The system according to claim 11, whereinthe electronic processor is configured to iteratively update, using aneural network, the internal states of the nodes by updating a value ina vector of values associated with the internal states of the nodes. 14.The system according to claim 13, wherein the values in the vector ofvalues include a value representing the brightness of a pixelcorresponding to the node and a value representing the internal state ofthe node.
 15. The system according to claim 11, wherein the electronicprocessor is further configured to perform, in each iteration, aconvolution involving previous internal states of the nodes.
 16. Thesystem according to claim 11, wherein the electronic processor isfurther configured to perform, in the first iteration, convolutions oneach value representing a brightness of each pixel.
 17. The systemaccording to claim 11, wherein the electronic processor is configured toidentify an object of interest within the image based on the values ofthe nodes at a convergence of the spatial lattice by using a final layerof the neural network to calculate a probability that each pixel isincluded in the object of interest based on the vector associated witheach pixel, and determining, for each pixel, if the calculatedprobability is above a predetermined threshold.
 18. The system accordingto claim 12, wherein the electronic processor is configured to updatethe internal state based on at least one selected from the groupconsisting of a value of the node from a previous iteration, a value ofa neighboring node from the previous iteration, or a new value of thenode by using a squashing function.
 19. The system according to claim12, wherein the neighboring node is one selected from a group consistingof a node that represents a pixel that is directly above, directlybelow, to the right of, and to the left of the pixel represented by thenode.
 20. Non-transitory computer-readable medium storing instructionsthat, when executed with an electronic processor, perform a set offunctions, the set of functions comprising: initializing internal statesof nodes of a spatial lattice, wherein each node represents a pixel ofan image and is connected to at least one neighboring pixel of theimage; iteratively updating, using a neural network, the internal statesof the nodes in the spatial lattice using spatially gated propagation,wherein at each iteration each node updates its internal state based onat least one selected from the group consisting of a value of the nodefrom a previous iteration, a value of a neighboring node from theprevious iteration, or a new value of the node; and identifying anobject of interest within the image based on the values of the nodes ata convergence of the spatial lattice.
 21. The non-transitorycomputer-readable medium according to claim 20, wherein iterativelyupdating, using a neural network, the internal states of the nodesincludes updating a value in a vector of values associated with theinternal states of the nodes.
 22. The non-transitory computer-readablemedium according to claim 20, wherein identifying an object of interestwithin the image based on the values of the nodes at a convergence ofthe spatial lattice includes using a final layer in the neural networkto calculate a probability that each pixel is included in the object ofinterest based on the vector associated with each pixel; anddetermining, for each pixel, if the calculated probability is above apredetermined threshold.